I need help solving partial fraction integration problem!?

Question

integrate : (s^4 + 81) / s(s^2 +9)^2 ds

I need help breaking this apart to
A/s + (Bs +C/ s^2 + 9) + (Ds + E / (S^2 +9)^2)

I keep getting stuck when I try to solve this. I don't even know if i am doing it right.

Thanks ahead for any help

Answer 1

first step right
multiply (both sides) throughout by:
s(s^2+9)^2
therefore:
s^4 +81=
A(s^2+9)^2 +(Bs+C)(s(s^2+9)^2)
+ (Ds+E)(s)
Now substitute values of 's'
on both sides to get the value of A B C D E
eg: first substitute "s=0"
therefore we get
81= A(9)^2 +0 +0
A=1

Answer 2

integrate : (s^4 + 81) / s(s^2 +9)^2 ds
(s^4 + 3^4)² over s(s² + 3²)² ds
(s² + 3²)(s² + 3²) over s(s² + 3²)(s² + 3²) ds =
1/s ds

Answer 3

undergo in concepts that (x^2-x-6) can be written as (x-3)(x+2). then you've got vital of a million/((x-3)(x+2)). For partial fractions, in simple terms talk despite is interior the vital. Write it out as: a million/(x-3)((x+2) = A/(x-3) + B/(x+2) you could sparkling up for A and B. to sparkling up for A, you could cancel its denominator (x-3) from the left area of the equation, so it particularly is going to develop right into a million/(x+2). to discover the fee of x, you utilize A's denominator: x-3=0, so x=3. So, a million/(3+2) = a million/5. it is the fee of A. in case you do a similar for B, you will get -a million/5. Now, somewhat of having a complicated vital, you have 2 easier problems: vital of (a million/5)/(x-3) + vital of (-a million/5)/(x+2). in case you carry out the constants outdoors the vital, then you would be wanting (a million/5) * vital (a million/(x-3)) - (a million/5)*vital(a million/(x+2)). wish this facilitates! :)